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Statistics & probability in CALCULA

CALCULA computes the descriptive statistics of a series, fits models, and evaluates probability distributions. Paste the values separated by spaces, commas or line breaks.

Describing a series

mean x̄ = (Σ xᵢ) / n · standard deviation σ = √( Σ(xᵢ − x̄)² / n )

The mean is pulled by extreme values; the median (the middle value) resists them. The standard deviation measures the spread around the mean. Divide by n for a whole population, by n − 1 for a sample.

Example

Series 4, 8, 15, 16, 23, 42: mean 18, median 15.5, standard deviation ≈ 12.4. The box plot shows that the middle half of the data sits between 8 and 23.

Linear regression

y = a·x + b with a = cov(x, y) / var(x)

The least-squares line minimises the sum of squared vertical distances. The coefficient of determination R² (between 0 and 1) says how much of the variation the model explains.

Probability distributions

CALCULA evaluates the usual distributions — binomial, Poisson, normal, exponential — and their quantiles. For the normal distribution, about 68 % of values fall within ±1 standard deviation of the mean, 95 % within ±2, 99.7 % within ±3.

Example

A test with 20 multiple-choice questions (4 options): answering at random, the number of correct answers follows a binomial distribution with mean 5 and standard deviation ≈ 1.9. Scoring 10/20 “by luck” has a probability below 1 %.

Typing it into CALCULA

Open the “≡” menu on “statistics”, paste the series or fill in the distribution's parameters. Results come with a histogram or a density curve. See also number theory.